CN115879357A - Self-adaptive bias proportion guidance method based on neural network - Google Patents

Abstract

The invention discloses a self-adaptive bias proportion guidance method based on a neural network, which aims at a static fixed target and utilizes the neural network to obtain a constant item in bias proportion guidance, wherein the neural network is a BP (back propagation) neural network, the input of the neural network is the missile eye distance, the initial ballistic inclination angle, the initial missile eye sight angle and the expected terminal intersection angle when an aircraft is launched, and the output is the constant item. The self-adaptive bias proportion guidance method based on the neural network is high in guidance precision, can complete parameter solution of bias proportion guidance on line under different initial conditions and constraints, and is flexible to use and low in calculation cost.

Description

An adaptive bias proportional guidance method based on neural network

Technical Field

The invention relates to an adaptive bias proportional guidance method based on a neural network, belonging to the technical field of aircraft control.

Background Art

The selection of guidance law plays a key role in the accuracy of the terminal intersection angle.

At present, the biased proportional navigation method is widely used. It adds a constant bias term to the traditional proportional navigation law. This method has the advantages of less required information and simple structure. In particular, there is no need to estimate the remaining flight time. Therefore, it has obvious advantages in engineering applications.

However, the accuracy of the bias term directly affects the guidance accuracy. The traditional formula has errors due to the small angle assumption used in the derivation and the formula used to estimate the total flight time, which affects the accuracy of the terminal intersection angle.

In addition, the traditional formula derivation method requires professional technicians to temporarily calculate and derive the bias terms based on the actual initial conditions. It has many usage restrictions and a large workload for calculation and derivation.

Due to the above reasons, it is necessary to propose a bias proportional guidance method with high accuracy that can be obtained quickly online.

Summary of the invention

In order to overcome the above problems, the inventors conducted in-depth research and designed an adaptive bias proportional guidance method based on a neural network. For a stationary fixed target, a neural network is used to obtain the constant term in the bias proportional guidance.

Furthermore, the neural network is a BP neural network.

In a preferred embodiment, the input of the neural network is the missile-target distance r, the initial trajectory inclination angle θ ₀ , the initial missile-target sight angle q ₀ and the expected terminal intersection angle θ _f when the aircraft is launched, and the output of the BP neural network is the constant term b.

In a preferred embodiment, the guidance law of the biased proportional guidance is obtained according to the following formula:

Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient.

In a preferred embodiment, the number of hidden layers of the BP neural network is 5.

In a preferred embodiment, the neural network needs to be trained before use, and trajectory simulation is used to obtain training samples.

In a preferred embodiment, the trajectory simulation is a nonlinear strike model simulation, and the nonlinear strike model can be expressed as:

η＝θ-q

Among them, η is the angle between the aircraft speed and the missile-target line of sight, θ is the trajectory inclination angle, q is the missile-target line of sight angle, r is the missile-target distance, v is the aircraft speed, and _aM is the overload command of the aircraft.

In a preferred embodiment, when establishing training samples, the setting parameters of the trajectory simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters. The setting parameters of the trajectory simulation include the initial projectile-target distance, the guidance coefficient, the initial trajectory inclination angle, and the initial projectile-target line of sight angle.

In a preferred embodiment, the initial projectile-target distance is 5000 meters to 10000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination angle is 10-20 degrees.

In a preferred embodiment, during the training of the neural network, the parameters of the neural network are updated using the Adam learning rate.

The beneficial effects of the present invention include:

(1) The BP neural network is used to achieve high-precision fitting approximation of the mapping, with high guidance accuracy;

(2) The bias proportional guidance parameter solution can be completed online under different initial conditions and constraints, which is flexible to use;

(3) It reduces the amount of calculation required to solve traditional formulas and reduces the computational cost in engineering applications.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 shows a schematic flow chart of an adaptive bias proportional guidance method based on a neural network according to a preferred embodiment of the present invention;

FIG2 shows the simulated ballistic trajectory of the guidance law in Example 1;

FIG3 shows the simulated trajectory inclination angle of the guidance law in Example 1;

FIG. 4 shows the simulated trajectory inclination angles in Example 2 and Comparative Example 1 according to the present invention.

DETAILED DESCRIPTION

The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

According to a neural network-based adaptive bias proportional guidance method provided by the present invention, a neural network is used to obtain bias proportional guidance for a stationary fixed target, thereby achieving precise footing constraint of an aircraft.

The guidance law of the biased proportional guidance can be expressed as:

Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, N is the guidance coefficient, and b is the bias term.

In traditional bias proportional guidance, the bias term is generally obtained using the following formula:

Among them, _θf is the terminal rendezvous angle, _θ0 is the initial trajectory inclination angle, _q0 is the initial missile-target line of sight angle, _t0 is the initial launch time of the aircraft, and _tf is the terminal rendezvous time of the aircraft.

There are the following traditional methods to obtain t _f -t ₀ :

t＝ _tf - _t0

Among them, t is the flight time taken by the aircraft from the start of launch to the flight to the target position; since _tf - _t0 applies the small angle assumption and the estimation of the remaining total flight time, it causes errors, resulting in the low accuracy of the guidance law of the biased proportional guidance finally obtained.

The inventors found that the error in t _f -t ₀ obtained by the traditional method can be compensated by adding the angle deviation term Δη and the time deviation term Δt:

均为正值，则|θ_f|是关于b的严格单调递增函数，而严格单调函数存在一一映射关系，即|θ_f|与b存在一一映射关系，可以表示为：Among them, r is the distance between the missile and the target, v is the speed of the aircraft,

are all positive values, then |θ _f | is a strictly monotone increasing function with respect to b, and a strictly monotone function has a one-to-one mapping relationship, that is, |θ _f | and b have a one-to-one mapping relationship, which can be expressed as:

b＝f ^-1 (r,N,q ₀ ,θ ₀ ,θ _f )

Furthermore, the BP neural network in the neural network can predict this mapping relationship more accurately. Therefore, in the present invention, the BP neural network is used to obtain the bias proportional guidance.

According to the present invention, the input of the neural network is the missile-target distance r, the initial trajectory inclination angle θ ₀ , the initial missile-target sight angle q ₀ and the desired terminal intersection angle θ _f when the aircraft is launched;

Different from the conventional method in which the constant term is obtained by solving the initial missile-target sight angle q ₀ , the initial trajectory inclination angle θ ₀ , the expected terminal intersection angle θ _f and the flight time t, in the present invention, the flight time t with a large error is no longer used as the input of the neural network, but the missile-target distance r which is easier to measure is used as the input of the neural network, thereby further improving the guidance accuracy.

Furthermore, the output of the BP neural network is a constant term b, and the guidance law of the bias proportional guidance is obtained according to the following formula:

Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient.

In a preferred embodiment, the number of hidden layers of the BP neural network is 5. The inventors found that when there are 5 hidden layers, the guidance law obtained based on the constant term output by the neural network is more accurate, and the calculation speed of the neural network is faster, which can achieve online solution.

Further preferably, the activation function of the BP neural network is a sigmoid function:

Furthermore, the BP neural network needs to be trained before use. In the present invention, trajectory simulation is used to obtain training samples.

Specifically, the trajectory simulation is a nonlinear strike model simulation, and the nonlinear strike model can be expressed as:

η＝θ-q

Among them, η is the angle between the aircraft speed and the missile-target line of sight, and a _M is the overload command of the aircraft.

Furthermore, the integral in the nonlinear strike model is solved by the Runge-Kutta method, and preferably, the solution step is 0.05.

The Runge-Kutta method is an important implicit or explicit iterative method for solving nonlinear ordinary differential equations, which will not be described in detail in the present invention.

Furthermore, when establishing the training samples, the setting parameters of the trajectory simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters.

Furthermore, the setting parameters of the trajectory simulation include an initial projectile-target distance, a guidance coefficient, an initial trajectory inclination angle, and an initial projectile-target sight angle.

In a preferred embodiment, in the setting parameters, the initial projectile-target distance is 5000 meters to 10000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination angle is 10-20 degrees.

In a preferred embodiment, a set of data is taken every 200 m of the initial projectile-target distance, the guidance coefficients are 2, 3, and 4 respectively, and a set of data is taken every 0.2° of the initial trajectory inclination angle as setting parameters for the trajectory simulation, thereby obtaining a more comprehensive training sample.

In a preferred embodiment, the setting parameters of the trajectory simulation in the training sample are adjusted according to the initial projectile-target distance. When the initial projectile-target distance is greater than 7500m, a set of data is taken at intervals of 100m, and the guidance coefficients are 2, 3, and 4 respectively, and a set of data is taken at intervals of 0.2° for the initial trajectory inclination angle as the setting parameters of the trajectory simulation, so as to ensure that the trained neural network can obtain better accuracy.

When the initial missile-target distance is less than 7500m, a set of data is taken at intervals of 200m, and the guidance coefficients are 2, 3, and 4 respectively. A set of data is taken at intervals of 0.2° for the initial trajectory inclination angle as the setting parameters for the trajectory simulation. Since the initial missile-target distance is relatively close, the sample size can be appropriately reduced while ensuring the guidance accuracy, thereby reducing the amount of computation of the neural network and the solving capability of the onboard computer, that is, there is no need for a high-configuration onboard computer, thus reducing costs.

According to the present invention, in the process of training a neural network, 60%-80% of the samples are selected from the training samples as training sets, for example, 70% of the samples are selected as training sets, 10%-20% of the samples are selected as test sets, for example, 15% of the samples are selected as test sets, and 10%-20% of the samples are selected as validation sets, for example, 15% of the samples are selected as validation sets.

Further preferably, in the process of training the neural network, the parameters of the neural network are updated using the Adam learning rate, and the updating process can be expressed as:

为更新前参数；

为更新后参数；κ为学习率；ε为平滑项，防止被零除；m′_t为一阶矩估计，v′_t为二阶矩估计；m_t为梯度一阶矩，v_t为梯度二阶矩，β₁、β₂为常值指数衰减率。in,

is the parameter before updating;

is the updated parameter; κ is the learning rate; ε is the smoothing term to prevent division by zero; m′ _t is the first-order moment estimate, v′ _t is the second-order moment estimate; m _t is the first-order moment of the gradient, v _t is the second-order moment of the gradient, β ₁ and β ₂ are constant exponential decay rates.

According to the present invention, the initial ballistic inclination angle of the aircraft when launched is preferably 10-20°. The inventors have found that the initial ballistic inclination angle has a great influence on the accuracy of the terminal intersection angle (i.e., the error between the actual terminal intersection angle and the expected terminal intersection angle). When the initial ballistic inclination angle is too small, the accuracy of the terminal intersection angle is significantly reduced. When the initial ballistic inclination angle is too large, it is not conducive to engineering launch and also affects the accuracy of the terminal intersection angle. More preferably, the initial ballistic inclination angle is 15-20°. Within this range, the accuracy of the terminal intersection angle is best.

Example

Example 1

Based on the neural network, the adaptive bias proportional guidance is obtained. The guidance law of the bias proportional guidance is:

The BP neural network is used to obtain the constant term b in the bias proportional guidance, where the number of hidden layers of the neural network is 5 and the activation function is the sigmoid function.

The training samples are obtained through ballistic simulation, which is a nonlinear strike model simulation. The nonlinear strike model is:

η＝θ-q

The integral in the nonlinear strike model is solved by the Runge-Kutta method with a solution step of 0.05. The setting parameters of the ballistic simulation include the initial projectile-target distance, guidance coefficient, initial ballistic inclination, and initial projectile-target line of sight angle. The initial projectile-target distance is 5000 meters to 10000 meters, the guidance coefficient is 2-4, the initial ballistic inclination is 10-20°, and a set of data is taken every 200 meters for the initial projectile-target distance. The guidance coefficients are 2, 3, and 4 respectively, and a set of data is taken every 0.2° for the initial ballistic inclination.

70% of the samples are selected from the training samples as the training set, 15% of the samples are selected as the test set, and 15% of the samples are selected as the validation set.

In the process of training the neural network, the Adam learning rate is used to update the parameters of the neural network. The update process is expressed as:

The trained BP neural network is used for simulation. The expected terminal intersection angle _θf in the simulation parameters is set to -30°, -60°, and -90° respectively. The other simulation parameters are shown in Table 1:

Table 1

According to the above parameters, the input parameters of the neural network are: projectile-target distance r=10000, initial trajectory inclination angle θ ₀ =10°, initial projectile-target sight angle q ₀ =0°, and the expected terminal intersection angles θ _f are -30°, -60°, and -90° respectively.

The biased proportional guidance law is obtained according to the BP neural network. The simulated ballistic trajectory of the guidance law is shown in Figure 2, and the ballistic inclination is shown in Figure 3. It can be seen from the figure that the aircraft can reach the target position in all three cases, and the actual terminal intersection angles are -29.9908°, -60.0016°, and -89.9976°, respectively, which are very close to the expected terminal intersection angle.

Example 2

The simulation is performed in the same manner as in Example 1, except that, in the simulation parameters, the expected terminal intersection angle _θf is set to -40° and -55° respectively, and the remaining simulation parameters are shown in Table 2:

Table 2

The ballistic inclination trajectory obtained by simulation is shown in Figure 4. The actual terminal intersection angles of the aircraft are -40.21 and -54.97° respectively.

Comparative Example 1

The same simulation experiment as in Example 2 is performed, except that the conventional formula is used to solve the guidance law of the offset proportional guidance. The simulated ballistic inclination angle of the guidance law is shown in FIG4 , and the actual terminal intersection angles of the aircraft are -41.95°-61.14°, respectively.

By comparing the simulated ballistic inclination angles of Example 2 and Comparative Example 1, it can be seen that the guidance law accuracy of the offset proportional guidance obtained in Example 2 is higher, and the error between the actual intersection angle and the expected intersection angle is reduced by more than 9 times, especially when the expected terminal intersection angle is large, the error between the actual intersection angle and the expected intersection angle is reduced by nearly 38 times, and the error between the actual intersection angle and the expected intersection angle is as low as 0.05%, and the guidance accuracy is significantly improved.

In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "back" and the like indicate positions or positional relationships based on the working state of the present invention, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", and "fourth" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims (10)

1. A neural network-based adaptive bias proportional guidance method, for a stationary fixed target, uses a neural network to obtain the constant term in the bias proportional guidance. 2. The method for adaptive bias proportional guidance based on neural network according to claim 1, characterized in that: The neural network is a BP neural network. 3. The method for adaptive bias proportional guidance based on neural network according to claim 1, characterized in that: The input of the neural network is the missile-target distance r, the initial trajectory inclination angle θ ₀ , the initial missile-target sight angle q ₀ and the expected terminal intersection angle θ _f when the aircraft is launched, and the output of the BP neural network is the constant term b. 4. The method for adaptive bias proportional guidance based on neural network according to claim 1, characterized in that: The guidance law of bias proportional guidance is obtained according to the following formula:

Among them, θ is the ballistic inclination angle, q is the sight angle between the projectile and the target, and N is the guidance coefficient. 5. The method for adaptive bias proportional guidance based on neural network according to claim 2, characterized in that: The number of hidden layers of the BP neural network is 5. 6. The method for adaptive bias proportional guidance based on neural network according to claim 1, characterized in that: Before using the neural network, it needs to be trained, and ballistic simulation is used to obtain training samples. 7. The method for adaptive bias proportional guidance based on neural network according to claim 6, characterized in that: The trajectory simulation is a nonlinear strike model simulation, and the nonlinear strike model can be expressed as:

η＝θ-q Among them, η is the angle between the aircraft speed and the missile-target line of sight, θ is the trajectory inclination angle, q is the missile-target line of sight angle, r is the missile-target distance, v is the aircraft speed, and _aM is the overload command of the aircraft. 8. The neural network-based adaptive bias proportional guidance method according to claim 6, characterized in that: When establishing training samples, the setting parameters of the trajectory simulation are modified multiple times to obtain the terminal intersection angle under different setting parameters. The setting parameters of the trajectory simulation include the initial projectile-target distance, the guidance coefficient, the initial trajectory inclination angle, and the initial projectile-target sight angle. 9. The method for adaptive bias proportional guidance based on neural network according to claim 6, characterized in that: The initial missile-target distance is 5000 meters to 10000 meters, the guidance coefficient is 2-4, and the initial ballistic inclination is 10-20°. 10. The method for adaptive bias proportional guidance based on neural network according to claim 1, characterized in that: In the process of training the neural network, the Adam learning rate is used to update the parameters of the neural network.

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